The origin of mutational epistasis.

The interconnected processes of protein folding, mutations, epistasis, and evolution have all been the subject of extensive analysis throughout the years due to their significance for structural and evolutionary biology. The origin (molecular basis) of epistasis-the non-additive interactions between mutations-is still, nonetheless, unknown. The existence of a new perspective on protein folding, a problem that needs to be conceived as an 'analytic whole', will enable us to shed light on the origin of mutational epistasis at the simplest level-within proteins-while also uncovering the reasons why the genetic background in which they occur, a key component of molecular evolution, could foster changes in epistasis effects. Additionally, because mutations are the source of epistasis, more research is needed to determine the impact of post-translational modifications, which can potentially increase the proteome's diversity by several orders of magnitude, on mutational epistasis and protein evolvability. Finally, a protein evolution thermodynamic-based analysis that does not consider specific mutational steps or epistasis effects will be briefly discussed. Our study explores the complex processes behind the evolution of proteins upon mutations, clearing up some previously unresolved issues, and providing direction for further research.

Analysis of proteins in the light of mutations.

Proteins have evolved through mutations-amino acid substitutions-since life appeared on Earth, some 109 years ago. The study of these phenomena has been of particular significance because of their impact on protein stability, function, and structure. This study offers a new viewpoint on how the most recent findings in these areas can be used to explore the impact of mutations on protein sequence, stability, and evolvability. Preliminary results indicate that: (1) mutations can be viewed as sensitive probes to identify 'typos' in the amino-acid sequence, and also to assess the resistance of naturally occurring proteins to unwanted sequence alterations; (2) the presence of 'typos' in the amino acid sequence, rather than being an evolutionary obstacle, could promote faster evolvability and, in turn, increase the likelihood of higher protein stability; (3) the mutation site is far more important than the substituted amino acid in terms of the marginal stability changes of the protein, and (4) the unpredictability of protein evolution at the molecular level-by mutations-exists even in the absence of epistasis effects. Finally, the Darwinian concept of evolution "descent with modification" and experimental evidence endorse one of the results of this study, which suggests that some regions of any protein sequence are susceptible to mutations while others are not. This work contributes to our general understanding of protein responses to mutations and may spur significant progress in our efforts to develop methods to accurately forecast changes in protein stability, their propensity for metamorphism, and their ability to evolve.

Rethinking the protein folding problem from a new perspective.

One of the main concerns of Anfinsen was to reveal the connection between the amino-acid sequence and their biologically active conformation. This search gave rise to two crucial questions in structural biology, namely, why the proteins fold and how a sequence encodes its folding. As to the why, he proposes a plausible answer, namely, the thermodynamic hypothesis. As to the how, this remains an unsolved challenge. Consequently, the protein folding problem is examined here from a new perspective, namely, as an 'analytic whole'. Conceiving the protein folding in this way enabled us to (i) examine in detail why the force-field-based approaches have failed, among other purposes, in their ability to predict the three-dimensional structure of a protein accurately; (ii) propose how to redefine them to prevent these shortcomings, and (iii) conjecture on the origin of the state-of-the-art numerical-methods success to predict the tridimensional structure of proteins accurately.

Exploring the quality of protein structural models from a Bayesian perspective.

We explore how ideas and practices common in Bayesian modeling can be applied to help assess the quality of 3D protein structural models. The basic premise of our approach is that the evaluation of a Bayesian statistical model's fit may reveal aspects of the quality of a structure when the fitted data is related to protein structural properties. Therefore, we fit a Bayesian hierarchical linear regression model to experimental and theoretical 13 Cα chemical shifts. Then, we propose two complementary approaches for the evaluation of such fitting: (a) in terms of the expected differences between experimental and posterior predicted values; (b) in terms of the leave-one-out cross-validation point-wise predictive accuracy. Finally, we present visualizations that can help interpret these evaluations. The analyses presented in this article are aimed to aid in detecting problematic residues in protein structures. The code developed for this work is available on: https://github.com/BIOS-IMASL/Hierarchical-Bayes-NMR-Validation.

The Marginal Stability of Proteins: How the Jiggling and Wiggling of Atoms is Connected to Neutral Evolution.

Here we propose that the upper bound marginal stability of proteins is a universal property that includes macro-molecular complexes and is not affected by molecular changes such as mutations and post-translational modifications. We theorize that its existence is a consequence of Afinsen's thermodynamic hypothesis rather than a result of an evolutionary process. This result enables us to conjecture that neutral evolution should also be, with respect to protein stability, a universal phenomenon.

Thermodynamics of cell penetrating peptides on lipid membranes: sequence and membrane acidity regulate surface binding.

Cell-penetrating peptides (CPPs) are molecules that traverse cell membranes and facilitate the cellular uptake of nano-sized cargoes. In this work we characterize the adsorption of amphipathic and purely cationic CPPs on membranes containing acidic lipids. We describe how the peptide primary sequence, the location of amino-acids within the sequence, the membrane composition, and the pH of the environment, determine both the surface concentration of the peptides and the molecular organization of the interface. Our results are obtained by applying a molecular theory that takes into account the size, shape, protonation state, charge distribution and conformational flexibility of the peptides, as well as the acid-base chemistry of the lipids. We find that peptide adsorption and binding free energy result from a balance between electrostatic and van der Waals interactions, and between chemical and entropic effective forces. We observe that, within a range of physiologically relevant parameters, acidic lipids respond to pH in ways that fully promote or deplete the surface accumulation of CPPs. Membrane acidity emerges thus as a crucial parameter to consider when designing CPP-based cargo-delivery vehicles.

Accounting for a mirror-image conformation as a subtle effect in protein folding.

By using local (free-energy profiles along the amino acid sequence and (13)C(α) chemical shifts) and global (principal component) analyses to examine the molecular dynamics of protein-folding trajectories, generated with the coarse-grained united-residue force field, for the B domain of staphylococcal protein A, we are able to (i) provide the main reason for formation of the mirror-image conformation of this protein, namely, a slow formation of the second loop and part of the third helix (Asp29-Asn35), caused by the presence of multiple local conformational states in this portion of the protein; (ii) show that formation of the mirror-image topology is a subtle effect resulting from local interactions; (iii) provide a mechanism for how protein A overcomes the barrier between the metastable mirror-image state and the native state; and (iv) offer a plausible reason to explain why protein A does not remain in the metastable mirror-image state even though the mirror-image and native conformations are at least energetically compatible.

Limiting Values of the one-bond C-H Spin-Spin Coupling Constants of the Imidazole Ring of Histidine at High-pH.

Assessment of the relative amounts of the forms of the imidazole ring of Histidine (His), namely the protonated (H+) and the tautomeric Nε2-H and Nδ1-H forms, respectively, is a challenging task in NMR spectroscopy. Indeed, their determination by direct observation of the 15N and 13C chemical shifts or the one-bond C-H, 1JCH, Spin-Spin Coupling Constants (SSCC) requires knowledge of the "canonical" limiting values of these forms in which each one is present to the extent of 100%. In particular, at high-pH, an accurate determination of these "canonical" limiting values, at which the tautomeric forms of His coexist, is an elusive problem in NMR spectroscopy. Among different NMR-based approaches to treat this problem, we focus here on the computation, at the DFT level of theory, of the high-pH limiting value for the 1JCH SSCC of the imidazole ring of His. Solvent effects were considered by using the polarizable continuum model approach. The results of this computation suggest, first, that the value of 1JCε1H = 205 ± 1.0 Hz should be adopted as the canonical high-pH limiting value for this SSCC; second, the variation of 1JCε1H SSCC during tautomeric changes is minor, i.e., within ±1Hz; and, finally, the value of 1JCδ2H SSCC upon tautomeric changes is large (15 Hz) indicating that, at high-pH or for non-protonated His at any pH, the tautomeric fractions of the imidazole ring of His can be predicted accurately as a function of the observed value of 1JCδ2H SSCC.

Azahar: a PyMOL plugin for construction, visualization and analysis of glycan molecules.

Glycans are key molecules in many physiological and pathological processes. As with other molecules, like proteins, visualization of the 3D structures of glycans adds valuable information for understanding their biological function. Hence, here we introduce Azahar, a computing environment for the creation, visualization and analysis of glycan molecules. Azahar is implemented in Python and works as a plugin for the well known PyMOL package (Schrodinger in The PyMOL molecular graphics system, version 1.3r1, 2010). Besides the already available visualization and analysis options provided by PyMOL, Azahar includes 3 cartoon-like representations and tools for 3D structure caracterization such as a comformational search using a Monte Carlo with minimization routine and also tools to analyse single glycans or trajectories/ensembles including the calculation of radius of gyration, Ramachandran plots and hydrogen bonds. Azahar is freely available to download from http://www.pymolwiki.org/index.php/Azahar and the source code is available at https://github.com/agustinaarroyuelo/Azahar .

Physics-based method to validate and repair flaws in protein structures.

A method that makes use of information provided by the combination of (13)C(α) and (13)C(ß) chemical shifts, computed at the density functional level of theory, enables one to (i) validate, at the residue level, conformations of proteins and detect backbone or side-chain flaws by taking into account an ensemble average of chemical shifts over all of the conformations used to represent a protein, with a sensitivity of ∼90%; and (ii) provide a set of (χ1/χ2) torsional angles that leads to optimal agreement between the observed and computed (13)C(α) and (13)C(ß) chemical shifts. The method has been incorporated into the CheShift-2 protein validation Web server. To test the reliability of the provided set of (χ1/χ2) torsional angles, the side chains of all reported conformations of five NMR-determined protein models were refined by a simple routine, without using NOE-based distance restraints. The refinement of each of these five proteins leads to optimal agreement between the observed and computed (13)C(α) and (13)C(ß) chemical shifts for ∼94% of the flaws, on average, without introducing a significantly large number of violations of the NOE-based distance restraints for a distance range ≤ 0.5 , in which the largest number of distance violations occurs. The results of this work suggest that use of the provided set of (χ1/χ2) torsional angles together with other observables, such as NOEs, should lead to a fast and accurate refinement of the side-chain conformations of protein models.

Are accurate computations of the 13C' shielding feasible at the DFT level of theory?

The goal of this study is twofold. First, to investigate the relative influence of the main structural factors affecting the computation of the (13)C' shielding, namely, the conformation of the residue itself and the next nearest-neighbor effects. Second, to determine whether calculation of the (13)C' shielding at the density functional level of theory (DFT), with an accuracy similar to that of the (13)C(α) shielding, is feasible with the existing computational resources. The DFT calculations, carried out for a large number of possible conformations of the tripeptide Ac-GXY-NMe, with different combinations of X and Y residues, enable us to conclude that the accurate computation of the (13)C' shielding for a given residue X depends on the: (i) (ϕ,ψ) backbone torsional angles of X; (ii) side-chain conformation of X; (iii) (ϕ,ψ) torsional angles of Y; and (iv) identity of residue Y. Consequently, DFT-based quantum mechanical calculations of the (13)C' shielding, with all these factors taken into account, are two orders of magnitude more CPU demanding than the computation, with similar accuracy, of the (13)C(α) shielding. Despite not considering the effect of the possible hydrogen bond interaction of the carbonyl oxygen, this work contributes to our general understanding of the main structural factors affecting the accurate computation of the (13)C' shielding in proteins and may spur significant progress in effort to develop new validation methods for protein structures.

Factors affecting the computation of the 13C shielding in disaccharides.

Knowledge of the three-dimensional structures of glycans and glycoproteins is useful for a full understanding of molecular processes in which glycans are involved, such as antigen-recognition and virus infection, to name a few. Among the ubiquitous nuclei in glycan molecules, the (13)C nucleus is an attractive candidate for computation of theoretical chemical shifts at the quantum chemical level of theory to validate and determine glycan structures. For this purpose, it is important to determine, first, which carbons can be used as probes to sense conformational changes and, second, all factors that affect the computation of the shielding, at the density functional theory (DFT) level of theory, of those carbons. To answer such questions, we performed a series of analyses on low-energy conformations, obtained by sampling the glycosidic torsional angles (ϕ, ψ) every 10°, of 12 disaccharides. Our results provide evidence that: (i) the carbons that participate in the glycosidic linkage are the most sensitive probes with which to sense conformational changes of disaccharides; (ii) the rotation of the hydroxyl groups closest to the glycosidic linkage significantly affects the computation of the shieldings of the carbons that participate in the glycosidic linkage; (iii) it is not possible to obtain the shieldings of one disaccharide from the computed values of a different disaccharide or from those disaccharides that differ in the anomeric state; and (iv) a proper basis set distribution, a functional, and a step size, with which to sample the conformational space, are necessary to compute shieldings accurately and rapidly.

Assessing the fractions of tautomeric forms of the imidazole ring of histidine in proteins as a function of pH.

A method is proposed to determine the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH, provided that the observed and chemical shifts and the protein structure, or the fraction of H(+) form, are known. This method is based on the use of quantum chemical methods to compute the (13)C NMR shieldings of all the imidazole ring carbons ((13)C(γ), , and ) for each of the two tautomers, N(δ1)-H and N(ε2)-H, and the protonated form, H(+), of histidine. This methodology enabled us (i) to determine the fraction of all the tautomeric forms of histidine for eight proteins for which the and chemical shifts had been determined in solution in the pH range of 3.2 to 7.5 and (ii) to estimate the fraction of tautomeric forms of eight histidine-containing dipeptide crystals for which the chemical shifts had been determined by solid-state (13)C NMR. Our results for proteins indicate that the protonated form is the most populated one, whereas the distribution of the tautomeric forms for the imidazole ring varies significantly among different histidines in the same protein, reflecting the importance of the environment of the histidines in determining the tautomeric forms. In addition, for ∼70% of the neutral histidine-containing dipeptides, the method leads to fairly good agreement between the calculated and the experimental tautomeric form. Coexistence of different tautomeric forms in the same crystal structure may explain the remaining 30% of disagreement.

CheShift-2: graphic validation of protein structures.

UNLABELLED: The differences between observed and predicted (13)C(α) chemical shifts can be used as a sensitive probe with which to detect possible local flaws in protein structures. For this reason, we previously introduced CheShift, a Web server for protein structure validation. Now, we present CheShift-2 in which a graphical user interface is implemented to render such local flaws easily visible. A series of applications to 15 ensembles of conformations illustrate the ability of CheShift-2 to locate the main structural flaws rapidly and accurately on a per-residue basis. Since accuracy plays a central role in CheShift predictions, the treatment of histidine (His) is investigated here by exploring which form of His should be used in CheShift-2. AVAILABILITY: CheShift-2 is free of charge for academic use and can be accessed from www.cheshift.com

Protein folding rate evolution upon mutations.

Despite the spectacular success of cutting-edge protein fold prediction methods, many critical questions remain unanswered, including why proteins can reach their native state in a biologically reasonable time. A satisfactory answer to this simple question could shed light on the slowest folding rate of proteins as well as how mutations-amino-acid substitutions and/or post-translational modifications-might affect it. Preliminary results indicate that (i) Anfinsen's dogma validity ensures that proteins reach their native state on a reasonable timescale regardless of their sequence or length, and (ii) it is feasible to determine the evolution of protein folding rates without accounting for epistasis effects or the mutational trajectories between the starting and target sequences. These results have direct implications for evolutionary biology because they lay the groundwork for a better understanding of why, and to what extent, mutations-a crucial element of evolution and a factor influencing it-affect protein evolvability. Furthermore, they may spur significant progress in our efforts to solve crucial structural biology problems, such as how a sequence encodes its folding.

Protein structure prediction from the complementary science perspective.

A comparative analysis between two problems-apparently unrelated-which are solved in a period of ~400 years, viz., the accurate prediction of both the planetary orbits and the protein structures, leads to inferred conjectures that go far beyond the existence of a common path in their resolution, i.e., observation → pattern recognition → modeling. The preliminary results from this analysis indicate that complementary science, together with a new perspective on protein folding, may help us discover common features that could contribute to a more in-depth understanding of still-unsolved problems such as protein folding.

CheShift-2 resolves a local inconsistency between two X-ray crystal structures.

Since chemical shifts provide important and relatively accessible information about protein structure in solution, a Web server, CheShift-2, was developed for structure interrogation, based on a quantum mechanics database of (13)C( α ) chemical shifts. We report the application of CheShift-2 to a local inconsistency between two X-ray crystal structures (PDB IDs 1IKN and 1NFI) of the complex between the p65/p50 heterodimer of NFκB and its inhibitor IκBα. The availability of NMR resonance assignments that included the region of the inconsistency provided an opportunity for independent validation of the CheShift-2 server. Application of the server showed that the (13)C( α ) chemical shifts measured for the Gly270-Pro281 sequence close to the C-terminus of IκBα were unequivocally consistent with the backbone structure modeled in the 1IKN structure, and were inconsistent with the 1NFI structure. Previous NOE measurements had demonstrated that the position of a tryptophan ring in the region immediately N-terminal in this region was not consistent with either structure. Subsequent recalculation of the local structure in this region, based on the electron density of the deposited structure factors for 1IKN, confirmed that the local backbone structure was best modeled by 1IKN, but that the rotamer of Trp258 is consistent with the 1NFI structure, including the presence of a hydrogen bond between the ring NεH of Trp258 and the backbone carbonyl group of Gln278. The consensus between all of these measures suggests that the CheShift-2 server operates well under circumstances in which backbone chemical shifts are available but where local plasticity may render X-ray structural data ambiguous.

Quantum-mechanics-derived 13Calpha chemical shift server (CheShift) for protein structure validation.

A server (CheShift) has been developed to predict (13)C(alpha) chemical shifts of protein structures. It is based on the generation of 696,916 conformations as a function of the phi, psi, omega, chi1 and chi2 torsional angles for all 20 naturally occurring amino acids. Their (13)C(alpha) chemical shifts were computed at the DFT level of theory with a small basis set and extrapolated, with an empirically-determined linear regression formula, to reproduce the values obtained with a larger basis set. Analysis of the accuracy and sensitivity of the CheShift predictions, in terms of both the correlation coefficient R and the conformational-averaged rmsd between the observed and predicted (13)C(alpha) chemical shifts, was carried out for 3 sets of conformations: (i) 36 x-ray-derived protein structures solved at 2.3 A or better resolution, for which sets of (13)C(alpha) chemical shifts were available; (ii) 15 pairs of x-ray and NMR-derived sets of protein conformations; and (iii) a set of decoys for 3 proteins showing an rmsd with respect to the x-ray structure from which they were derived of up to 3 A. Comparative analysis carried out with 4 popular servers, namely SHIFTS, SHIFTX, SPARTA, and PROSHIFT, for these 3 sets of conformations demonstrated that CheShift is the most sensitive server with which to detect subtle differences between protein models and, hence, to validate protein structures determined by either x-ray or NMR methods, if the observed (13)C(alpha) chemical shifts are available. CheShift is available as a web server.

Proteins' Evolution upon Point Mutations.

As the reader must be already aware, state-of-the-art protein folding prediction methods have reached a smashing success in their goal of accurately determining the three-dimensional structures of proteins. Yet, a solution to simple problems such as the effects of protein point mutations on their (i) native conformation; (ii) marginal stability; (iii) ensemble of high-energy nativelike conformations; and (iv) metamorphism propensity and, hence, their evolvability, remains as an unsolved problem. As a plausible solution to the latter, some properties of the amide hydrogen-deuterium exchange, a highly sensitive probe of the structure, stability, and folding of proteins, are assessed from a new perspective. The preliminary results indicate that the protein marginal stability change upon point mutations provides the necessary and sufficient information to estimate, through a Boltzmann factor, the evolution of the amide hydrogen exchange protection factors and, consequently, that of the ensemble of folded conformations coexisting with the native state. This work contributes to our general understanding of the effects of point mutations on proteins and may spur significant progress in our efforts to develop methods to determine the appearance of new folds and functions accurately.

Use of 13C(alpha) chemical shifts for accurate determination of beta-sheet structures in solution.

A physics-based method, aimed at determining protein structures by using NOE-derived distance constraints together with observed and computed 13C(alpha) chemical shifts, is applied to determine the structure of a 20-residue all-beta peptide (BS2). The approach makes use of 13C(alpha) chemical shifts, computed at the density functional level of theory, to derive backbone and side-chain torsional constraints for all of the amino acid residues, without making use of information about residue occupancy in any region of the Ramachandran map. In addition, the torsional constraints are derived dynamically--i.e., they are redefined at each step of the algorithm. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than existing NMR-derived models of the peptide, in terms of the agreement between predicted and observed 13C(beta) chemical shifts, and some stereochemical quality indicators. The accumulated evidence indicates that, for a highly flexible BS2 peptide in solution, it may not be possible to determine a single structure (or a small set of structures) that would satisfy all of the constraints exactly and simultaneously because the observed NOEs and 13C(alpha) chemical shifts correspond to a dynamic ensemble of conformations. Analysis of the structural flexibility, carried out by molecular dynamics simulations in explicit water, revealed that the whole peptide can be characterized as having liquid-like behavior, according to the Lindemann criterion. In summary, a beta-sheet structure of a highly flexible peptide in solution can be determined by a quantum-chemical-based procedure.